0000000000309118
AUTHOR
A. S. Dmitrichev
Polymorphic and regular localized activity structures in a two-dimensional two-component reaction–diffusion lattice with complex threshold excitation
Abstract Space–time dynamics of the system modeling collective behaviour of electrically coupled nonlinear units is investigated. The dynamics of a local cell is described by the FitzHugh–Nagumo system with complex threshold excitation. It is shown that such a system supports formation of two distinct kinds of stable two-dimensional spatially localized moving structures without any external stabilizing actions. These are regular and polymorphic structures. The regular structures preserve their shape and velocity under propagation while the shape and velocity as well as other integral characteristics of polymorphic structures show rather complex temporal behaviour. Both kinds of structures r…
Heteroclinic contours and self-replicated solitary waves in a reaction–diffusion lattice with complex threshold excitation
Abstract The space–time dynamics of the network system modeling collective behavior of electrically coupled nonlinear cells is investigated. The dynamics of a local cell is described by the FitzHugh–Nagumo system with complex threshold excitation. Heteroclinic orbits defining traveling wave front solutions are investigated in a moving frame system. A heteroclinic contour formed by separatrix manifolds of two saddle-foci is found in the phase space. The existence of such structure indicates the appearance of complex wave patterns in the network. Such solutions have been confirmed and analyzed numerically. Complex homoclinic orbits found in the neighborhood of the heteroclinic contour define …